SME
Principles of Biology I · Problem type
Length of mitosis from the mitotic index
Use this for “Of 400 root tip cells, 20 are in mitosis. How long does mitosis last in a 24 h cycle?”
Chart
20 + 380 = 400.
This is an example. Type your own values to start a new problem.
t (h)
=
m
N
×
T (h)
N is every cell counted, both slices of the pie, and T is the length of one whole cell cycle.
i
Cells in interphase
worked out (not typed)
MI
Mitotic index
calculated · %
Formulas
i
=
N
−
m
380 = 400 − 20
MI
=
100
×
m
N
5
=
100
×
20
400
t
=
MI
100
×
T
1.2
=
5
100
×
24
Assumptions
•
The cells divide out of step, so the share of cells caught in a phase is that phase’s share of the cycle.
•
The mitotic index is the percent of the cells counted that are in prophase to telophase.
•
Every cell counted is cycling: none has stopped in G₀.
Step-by-step
WE KNOW
m = 20, N = 400, T = 24 h
FIND
cells in interphase (i), mitotic index (MI), time in mitosis (t)
Step 1 · Find cells in interphase (i)
Use i = N − m
Every cell counted that is not in mitosis is in interphase.
i
=
400
−
20
i
=
380
Step 2 · Find mitotic index (MI)
Use MI = 100 × m ÷ N
The cells in mitosis as a percent of all the cells counted.
MI
=
100
×
20
400
MI
=
2,000
400
MI = 5%
Step 3 · Find time in mitosis (t)
Use t = MI ÷ 100 × T
The share of cells in mitosis is the share of the cycle spent in mitosis.
t
=
5
100
×
24
t
=
0.05
×
24
t
=
1.2
h
Check
Put the numbers back in. Both sides should match.
380 = 400 − 20 ✓
5
=
100
×
20
400
✓
1.2
=
5
100
×
24
✓
Topic check
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